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Select all of the true statements.\newlineMulti-select Choices:\newline(A) 1×1021 \times 10^{-2} is 5050 times as much as 2×1042 \times 10^{-4}.\newline(B) 8×1028 \times 10^{2} is 0.020.02 times as much as 4×1044 \times 10^{4}.\newline(C) 3×1033 \times 10^{-3} is 66 times as much as 5×1025 \times 10^{-2}.\newline(D) 8×1098 \times 10^{9} is 505000 times as much as 505011.

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Q. Select all of the true statements.\newlineMulti-select Choices:\newline(A) 1×1021 \times 10^{-2} is 5050 times as much as 2×1042 \times 10^{-4}.\newline(B) 8×1028 \times 10^{2} is 0.020.02 times as much as 4×1044 \times 10^{4}.\newline(C) 3×1033 \times 10^{-3} is 66 times as much as 5×1025 \times 10^{-2}.\newline(D) 8×1098 \times 10^{9} is 505000 times as much as 505011.
  1. Check (A): To check (A), compare 1×1021 \times 10^{-2} and 2×1042 \times 10^{-4}. Calculate 5050 times 2×1042 \times 10^{-4} to see if it equals 1×1021 \times 10^{-2}. \newline50×(2×104)=100×104=1×10250 \times (2 \times 10^{-4}) = 100 \times 10^{-4} = 1 \times 10^{-2}. \newlineSo, (A) is true.
  2. Check (B): For (B), compare 8×1028 \times 10^2 and 4×1044 \times 10^4. Calculate 0.02×4×1040.02 \times 4 \times 10^4 to see if it equals 8×1028 \times 10^2.\newline0.02×(4×104)=0.08×104=8×1020.02 \times (4 \times 10^4) = 0.08 \times 10^4 = 8 \times 10^2.\newlineSo, (B) is true.
  3. Check (C): To check (C), compare 3×1033 \times 10^{-3} and 5×1025 \times 10^{-2}. Calculate 66 times 5×1025 \times 10^{-2} to see if it equals 3×1033 \times 10^{-3}. \newline6×(5×102)=30×1026 \times (5 \times 10^{-2}) = 30 \times 10^{-2}. \newlineThis does not equal 3×1033 \times 10^{-3}, so (C) is false.
  4. Check (D): For (D), compare 8×1098 \times 10^9 and 4×1064 \times 10^6. Calculate 2,000×4×1062,000 \times 4 \times 10^6 to see if it equals 8×1098 \times 10^9.\newline2,000×(4×106)=8,000×106=8×1092,000 \times (4 \times 10^6) = 8,000 \times 10^6 = 8 \times 10^9.\newlineSo, (D) is true.

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